Decorrelation-Based Feature Discovery: LGG_Radiomics-Whole
Jose Tamez
2023-09-15
- 1 Effect of UPSTM-Based Decorrelation
on Feature Discovery
- 1.0.1 Loading the libraries
- 1.1 Material and Methods
- 1.2 The Data
- 1.3 Generaring the report
- 1.4 The heatmap of the data
- 1.5 The decorrelation
- 1.6 The heatmap of the decorrelated data
- 1.7 The correlation matrix after decorrelation
- 1.8 U-MAP Visualization of features
- 1.9 Univariate Analysis
- 1.10 Comparing IDeA vs PCA vs EFA
- 1.11 Effect on CAR modeling
1 Effect of UPSTM-Based Decorrelation on Feature Discovery
1.0.1 Loading the libraries
library("FRESA.CAD")
library(readxl)
library(igraph)
library(umap)
library(tsne)
library(entropy)
op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)1.1 Material and Methods
About Dataset This dataset is a copy of another Kaggle dataset which can be accessed here: https://www.kaggle.com/c/glioma-radiomics The difference is that I have provided ground truth for the test set (test_GT.csv).
The suffix “omics” in Medical Science is associated with analysis of big sets of features (e.g. Genomics, Proteomics). Radiomics are imaging features (e.g., first order and second order) extracted from Regions of Interest (ROI) in radiology images based on predefined functions and filters. Low grade gliomas (LGG) are a type of brain tumors. Astrocytes and Oligodendrocytes which are two types of brain cells, are considered as origins of LGG. Adult LGG are characterized by different mutations which is important to be correctly identified. With this dataset the goal is to determine if an ROI has 1p19q codeletion (Mutacion=1) or not(Mutacion=0). This plays a key role in predicting patient’s response to chemotherapy and their survival. The dataset provides 640 different radiomics features for each ROI. There are 105 ROIs in the training set and 45 ROIs in the test cohort.
1.2 The Data
https://www.kaggle.com/datasets/knamdar/radiomics-for-lgg-dataset?select=test_GT.csv
LGG_Data <- read.csv("~/GitHub/LatentBiomarkers/Data/LGG/train.csv")
LGG_DataTest <- read.csv("~/GitHub/LatentBiomarkers/Data/LGG/test.csv")
LGG_TestGT <- read.csv("~/GitHub/LatentBiomarkers/Data/LGG/test_GT.csv")
LGG_DataTest$Mutacion <- LGG_TestGT$Mutacion
LGG_Data <- rbind(LGG_Data,LGG_DataTest)
rownames(LGG_Data) <- LGG_Data$patientID
LGG_Data$patientID <- NULL
pander::pander(table(LGG_Data$Mutacion))| 0 | 1 |
|---|---|
| 54 | 96 |
1.2.0.1 Standarize the names for the reporting
studyName <- "LGG"
dataframe <- LGG_Data
outcome <- "Mutacion"
TopVariables <- 10
thro <- 0.80
cexheat = 0.151.3 Generaring the report
1.3.1 Libraries
Some libraries
library(psych)
library(whitening)
library("vioplot")
library("rpart")1.3.2 Data specs
pander::pander(c(rows=nrow(dataframe),col=ncol(dataframe)-1))| rows | col |
|---|---|
| 150 | 640 |
pander::pander(table(dataframe[,outcome]))| 0 | 1 |
|---|---|
| 54 | 96 |
varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]
largeSet <- length(varlist) > 1500 1.3.3 Scaling the data
Scaling and removing near zero variance columns and highly co-linear(r>0.99999) columns
### Some global cleaning
sdiszero <- apply(dataframe,2,sd) > 1.0e-16
dataframe <- dataframe[,sdiszero]
varlist <- colnames(dataframe)[colnames(dataframe) != outcome]
tokeep <- c(as.character(correlated_Remove(dataframe,varlist,thr=0.99999)),outcome)
dataframe <- dataframe[,tokeep]
varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]
iscontinous <- sapply(apply(dataframe,2,unique),length) >= 5 ## Only variables with enough samples
dataframeScaled <- FRESAScale(dataframe,method="OrderLogit")$scaledData1.4 The heatmap of the data
numsub <- nrow(dataframe)
if (numsub > 1000) numsub <- 1000
if (!largeSet)
{
hm <- heatMaps(data=dataframeScaled[1:numsub,],
Outcome=outcome,
Scale=TRUE,
hCluster = "row",
xlab="Feature",
ylab="Sample",
srtCol=45,
srtRow=45,
cexCol=cexheat,
cexRow=cexheat
)
par(op)
}
1.4.0.1 Correlation Matrix of the Data
The heat map of the data
if (!largeSet)
{
par(cex=0.6,cex.main=0.85,cex.axis=0.7)
#cormat <- Rfast::cora(as.matrix(dataframe[,varlist]),large=TRUE)
cormat <- cor(dataframe[,varlist],method="pearson")
cormat[is.na(cormat)] <- 0
gplots::heatmap.2(abs(cormat),
trace = "none",
# scale = "row",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "Original Correlation",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
key.title=NA,
key.xlab="|Pearson Correlation|",
xlab="Feature", ylab="Feature")
diag(cormat) <- 0
print(max(abs(cormat)))
}
[1]
0.9999991
1.5 The decorrelation
DEdataframe <- IDeA(dataframe,verbose=TRUE,thr=thro)
#>
#> Included: 633 , Uni p: 0.02486647 , Uncorrelated Base: 57 , Outcome-Driven Size: 0 , Base Size: 57
#>
#>
1 <R=1.000,r=0.975,N= 394>, Top: 93( 3 )[ 1 : 93 Fa= 91 : 0.975 ]( 91 , 235 , 0 ),<|>Tot Used: 326 , Added: 235 , Zero Std: 0 , Max Cor: 1.000
#>
2 <R=1.000,r=0.975,N= 394>, Top: 40( 1 )[ 1 : 40 Fa= 131 : 0.975 ]( 40 , 76 , 91 ),<|>Tot Used: 366 , Added: 76 , Zero Std: 0 , Max Cor: 1.000
#>
3 <R=1.000,r=0.975,N= 394>, Top: 4( 3 )[ 1 : 4 Fa= 135 : 0.975 ]( 4 , 13 , 131 ),<|>Tot Used: 377 , Added: 13 , Zero Std: 0 , Max Cor: 0.983
#>
4 <R=0.983,r=0.941,N= 202>, Top: 71( 1 )[ 1 : 71 Fa= 165 : 0.941 ]( 68 , 104 , 135 ),<|>Tot Used: 453 , Added: 104 , Zero Std: 0 , Max Cor: 0.998
#>
5 <R=0.998,r=0.949,N= 202>, Top: 7( 1 )[ 1 : 7 Fa= 168 : 0.949 ]( 7 , 10 , 165 ),<|>Tot Used: 456 , Added: 10 , Zero Std: 0 , Max Cor: 0.954
#>
6 <R=0.954,r=0.877,N= 188>, Top: 69( 1 )=[ 2 : 69 Fa= 189 : 0.930 ]( 66 , 90 , 168 ),<|>Tot Used: 500 , Added: 90 , Zero Std: 0 , Max Cor: 0.977
#>
7 <R=0.977,r=0.888,N= 188>, Top: 20( 1 )[ 1 : 20 Fa= 196 : 0.888 ]( 20 , 24 , 189 ),<|>Tot Used: 507 , Added: 24 , Zero Std: 0 , Max Cor: 0.899
#>
8 <R=0.899,r=0.849,N= 188>, Top: 49( 1 )[ 1 : 49 Fa= 213 : 0.849 ]( 49 , 57 , 196 ),<|>Tot Used: 533 , Added: 57 , Zero Std: 0 , Max Cor: 1.000
#>
9 <R=1.000,r=0.900,N= 188>, Top: 8( 1 )[ 1 : 8 Fa= 217 : 0.900 ]( 8 , 8 , 213 ),<|>Tot Used: 535 , Added: 8 , Zero Std: 0 , Max Cor: 0.992
#>
10 <R=0.992,r=0.846,N= 28>, Top: 14( 1 )[ 1 : 14 Fa= 221 : 0.846 ]( 14 , 14 , 217 ),<|>Tot Used: 539 , Added: 14 , Zero Std: 0 , Max Cor: 0.992
#>
11 <R=0.992,r=0.846,N= 28>, Top: 3( 1 )[ 1 : 3 Fa= 222 : 0.846 ]( 3 , 3 , 221 ),<|>Tot Used: 539 , Added: 3 , Zero Std: 0 , Max Cor: 0.992
#>
12 <R=0.992,r=0.846,N= 28>, Top: 1( 1 )[ 1 : 1 Fa= 222 : 0.846 ]( 1 , 1 , 222 ),<|>Tot Used: 539 , Added: 1 , Zero Std: 0 , Max Cor: 0.992
#>
13 <R=0.992,r=0.800,N= 146>, Top: 55( 1 )[ 1 : 55 Fa= 237 : 0.800 ]( 54 , 77 , 222 ),<|>Tot Used: 563 , Added: 77 , Zero Std: 0 , Max Cor: 0.992
#>
14 <R=0.992,r=0.800,N= 146>, Top: 15( 1 )[ 1 : 15 Fa= 238 : 0.800 ]( 15 , 16 , 237 ),<|>Tot Used: 564 , Added: 16 , Zero Std: 0 , Max Cor: 0.992
#>
15 <R=0.992,r=0.800,N= 146>, Top: 6( 1 )[ 1 : 6 Fa= 239 : 0.800 ]( 6 , 7 , 238 ),<|>Tot Used: 564 , Added: 7 , Zero Std: 0 , Max Cor: 0.992
#>
16 <R=0.992,r=0.800,N= 2>, Top: 1( 1 )[ 1 : 1 Fa= 239 : 0.800 ]( 1 , 1 , 239 ),<|>Tot Used: 564 , Added: 1 , Zero Std: 0 , Max Cor: 0.992
#>
17 <R=0.992,r=0.800,N= 2>, Top: 1( 1 )[ 1 : 1 Fa= 239 : 0.800 ]( 1 , 1 , 239 ),<|>Tot Used: 564 , Added: 1 , Zero Std: 0 , Max Cor: 0.992
#>
18 <R=0.992,r=0.800,N= 2>, Top: 1( 1 )[ 1 : 1 Fa= 239 : 0.800 ]( 1 , 1 , 239 ),<|>Tot Used: 564 , Added: 1 , Zero Std: 0 , Max Cor: 0.992
#>
19 <R=0.992,r=0.800,N= 2>, Top: 1( 1 )[ 1 : 1 Fa= 239 : 0.800 ]( 1 , 1 , 239 ),<|>Tot Used: 564 , Added: 1 , Zero Std: 0 , Max Cor: 0.992
#>
20 <R=0.992,r=0.800,N= 2>, Top: 1( 1 )[ 1 : 1 Fa= 239 : 0.800 ]( 1 , 1 , 239 ),<|>Tot Used: 564 , Added: 1 , Zero Std: 0 , Max Cor: 0.992
#>
21 <R=0.992,r=0.800,N= 2>, Top: 1( 1 )[ 1 : 1 Fa= 239 : 0.800 ]( 1 , 1 , 239 ),<|>Tot Used: 564 , Added: 1 , Zero Std: 0 , Max Cor: 0.992
#>
22 <R=0.992,r=0.800,N= 2>, Top: 1( 1 )[ 1 : 1 Fa= 239 : 0.800 ]( 1 , 1 , 239 ),<|>Tot Used: 564 , Added: 1 , Zero Std: 0 , Max Cor: 0.992
#>
23 <R=0.992,r=0.800,N= 2>, Top: 1( 1 )[ 1 : 1 Fa= 239 : 0.800 ]( 1 , 1 , 239 ),<|>Tot Used: 564 , Added: 1 , Zero Std: 0 , Max Cor: 0.989
#>
24 <R=0.989,r=0.800,N= 2>, Top: 1( 1 )[ 1 : 1 Fa= 239 : 0.800 ]( 1 , 1 , 239 ),<|>Tot Used: 564 , Added: 1 , Zero Std: 0 , Max Cor: 0.833
#>
25 <R=0.833,r=0.800,N= 2>, Top: 1( 1 )[ 1 : 1 Fa= 239 : 0.800 ]( 1 , 1 , 239 ),<|>Tot Used: 564 , Added: 1 , Zero Std: 0 , Max Cor: 0.800
#>
26 <R=0.800,r=0.800,N= 2>
#>
[ 26 ], 0.7999294 Decor Dimension: 564 Nused: 564 . Cor to Base: 220 , ABase: 19 , Outcome Base: 0
#>
varlistc <- colnames(DEdataframe)[colnames(DEdataframe) != outcome]
pander::pander(sum(apply(dataframe[,varlist],2,var)))6.77e+22
pander::pander(sum(apply(DEdataframe[,varlistc],2,var)))6.77e+22
pander::pander(entropy(discretize(unlist(dataframe[,varlist]), 256)))0.000131
pander::pander(entropy(discretize(unlist(DEdataframe[,varlistc]), 256)))0.000131
1.5.1 The decorrelation matrix
if (!largeSet)
{
par(cex=0.6,cex.main=0.85,cex.axis=0.7)
UPSTM <- attr(DEdataframe,"UPSTM")
gplots::heatmap.2(1.0*(abs(UPSTM)>0),
trace = "none",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "Decorrelation matrix",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
key.title=NA,
key.xlab="|Beta|>0",
xlab="Output Feature", ylab="Input Feature")
par(op)
}
1.6 The heatmap of the decorrelated data
if (!largeSet)
{
hm <- heatMaps(data=DEdataframe[1:numsub,],
Outcome=outcome,
Scale=TRUE,
hCluster = "row",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
xlab="Feature",
ylab="Sample")
par(op)
}
1.7 The correlation matrix after decorrelation
if (!largeSet)
{
cormat <- cor(DEdataframe[,varlistc],method="pearson")
cormat[is.na(cormat)] <- 0
gplots::heatmap.2(abs(cormat),
trace = "none",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "Correlation after IDeA",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
key.title=NA,
key.xlab="|Pearson Correlation|",
xlab="Feature", ylab="Feature")
par(op)
diag(cormat) <- 0
print(max(abs(cormat)))
}
[1]
0.7999294
1.8 U-MAP Visualization of features
1.8.1 The UMAP based on LASSO on Raw Data
if (nrow(dataframe) < 1000)
{
classes <- unique(dataframe[1:numsub,outcome])
raincolors <- rainbow(length(classes))
names(raincolors) <- classes
datasetframe.umap = umap(scale(dataframe[1:numsub,varlist]),n_components=2)
plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: Original",t='n')
text(datasetframe.umap$layout,labels=dataframe[1:numsub,outcome],col=raincolors[dataframe[1:numsub,outcome]+1])
}
1.8.2 The decorralted UMAP
if (nrow(dataframe) < 1000)
{
datasetframe.umap = umap(scale(DEdataframe[1:numsub,varlistc]),n_components=2)
plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: After IDeA",t='n')
text(datasetframe.umap$layout,labels=DEdataframe[1:numsub,outcome],col=raincolors[DEdataframe[1:numsub,outcome]+1])
}
1.9 Univariate Analysis
1.9.1 Univariate
univarRAW <- uniRankVar(varlist,
paste(outcome,"~1"),
outcome,
dataframe,
rankingTest="AUC")100 : wavelet.HHH_firstorder_10Percentile 200 :
wavelet.HHL_firstorder_Uniformity 300 : wavelet.HLH_glcm_Imc1 400 :
wavelet.HLL_gldm_GrayLevelVariance 500 :
wavelet.LHH_glrlm_LongRunLowGrayLevelEmphasis
600 : wavelet.LHL_glszm_LargeAreaHighGrayLevelEmphasis
univarDe <- uniRankVar(varlistc,
paste(outcome,"~1"),
outcome,
DEdataframe,
rankingTest="AUC",
)100 : La_wavelet.HHH_firstorder_10Percentile 200 :
La_wavelet.HHL_firstorder_Uniformity 300 : La_wavelet.HLH_glcm_Imc1 400
: La_wavelet.HLL_gldm_GrayLevelVariance 500 :
La_wavelet.LHH_glrlm_LongRunLowGrayLevelEmphasis
600 : La_wavelet.LHL_glszm_LargeAreaHighGrayLevelEmphasis
1.9.2 Final Table
univariate_columns <- c("caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC")
##top variables
topvar <- c(1:length(varlist)) <= TopVariables
tableRaw <- univarRAW$orderframe[topvar,univariate_columns]
pander::pander(tableRaw)| caseMean | caseStd | controlMean | controlStd | controlKSP | ROCAUC | |
|---|---|---|---|---|---|---|
| original_firstorder_Skewness | -3.93e-02 | 5.28e-01 | -6.84e-01 | 6.34e-01 | 9.78e-01 | 0.780 |
| original_glcm_ClusterShade | 7.42e+02 | 1.02e+04 | -1.06e+04 | 1.65e+04 | 4.41e-02 | 0.755 |
| wavelet.HLL_glcm_ClusterShade | -7.99e+02 | 3.12e+03 | 2.32e+03 | 4.29e+03 | 4.72e-02 | 0.737 |
| wavelet.HLL_firstorder_Skewness | -1.05e-02 | 5.50e-01 | 5.21e-01 | 8.55e-01 | 5.54e-02 | 0.736 |
| original_firstorder_Median | 2.77e+02 | 5.52e+01 | 3.33e+02 | 8.63e+01 | 6.29e-01 | 0.732 |
| original_glcm_MaximumProbability | 6.19e-03 | 2.32e-03 | 1.02e-02 | 6.26e-03 | 7.10e-02 | 0.722 |
| original_gldm_LargeDependenceHighGrayLevelEmphasis | 1.36e+04 | 9.87e+03 | 3.19e+04 | 3.44e+04 | 2.54e-03 | 0.711 |
| original_glcm_JointEnergy | 1.72e-03 | 7.60e-04 | 2.89e-03 | 2.23e-03 | 1.21e-02 | 0.710 |
| original_firstorder_Mean | 2.75e+02 | 5.33e+01 | 3.20e+02 | 7.86e+01 | 3.40e-01 | 0.702 |
| original_glszm_LargeAreaHighGrayLevelEmphasis | 2.34e+04 | 4.63e+04 | 1.77e+05 | 7.31e+05 | 1.50e-08 | 0.700 |
topLAvar <- univarDe$orderframe$Name[str_detect(univarDe$orderframe$Name,"La_")]
topLAvar <- unique(c(univarDe$orderframe$Name[topvar],topLAvar[1:as.integer(TopVariables/2)]))
finalTable <- univarDe$orderframe[topLAvar,univariate_columns]
pander::pander(finalTable)| caseMean | caseStd | controlMean | controlStd | controlKSP | ROCAUC | |
|---|---|---|---|---|---|---|
| original_firstorder_Skewness | -0.0393 | 5.28e-01 | -6.84e-01 | 6.34e-01 | 0.9782 | 0.780 |
| La_wavelet.HLL_glszm_SmallAreaHighGrayLevelEmphasis | -55.1442 | 5.85e+01 | 2.27e+01 | 1.23e+02 | 0.0420 | 0.762 |
| La_wavelet.LHL_glszm_GrayLevelNonUniformity | 9.5446 | 7.66e+00 | 2.05e+00 | 6.86e+00 | 0.5629 | 0.761 |
| original_glcm_ClusterShade | 741.5044 | 1.02e+04 | -1.06e+04 | 1.65e+04 | 0.0441 | 0.755 |
| La_wavelet.HLL_firstorder_RobustMeanAbsoluteDeviation | -0.0545 | 7.68e-01 | 6.93e-01 | 1.20e+00 | 0.0869 | 0.746 |
| La_wavelet.LHL_firstorder_10Percentile | 89.3291 | 5.91e+00 | 8.29e+01 | 8.62e+00 | 0.1136 | 0.744 |
| wavelet.HLL_glcm_ClusterShade | -799.0582 | 3.12e+03 | 2.32e+03 | 4.29e+03 | 0.0472 | 0.737 |
| wavelet.HLL_firstorder_Skewness | -0.0105 | 5.50e-01 | 5.21e-01 | 8.55e-01 | 0.0554 | 0.736 |
| La_wavelet.HLL_gldm_DependenceNonUniformity | 187.7064 | 1.34e+02 | 6.86e+01 | 1.35e+02 | 0.7199 | 0.734 |
| La_wavelet.HLL_gldm_HighGrayLevelEmphasis | -23.1086 | 3.90e+01 | -6.66e+01 | 6.62e+01 | 0.3168 | 0.731 |
dc <- getLatentCoefficients(DEdataframe)
fscores <- attr(DEdataframe,"fscore")
pander::pander(c(mean=mean(sapply(dc,length)),total=length(dc),fraction=length(dc)/(ncol(dataframe)-1)))| mean | total | fraction |
|---|---|---|
| 2.53 | 504 | 0.796 |
theCharformulas <- attr(dc,"LatentCharFormulas")
finalTable <- rbind(finalTable,tableRaw[topvar[!(topvar %in% topLAvar)],univariate_columns])
orgnamez <- rownames(finalTable)
orgnamez <- str_remove_all(orgnamez,"La_")
finalTable$RAWAUC <- univarRAW$orderframe[orgnamez,"ROCAUC"]
finalTable$DecorFormula <- theCharformulas[rownames(finalTable)]
finalTable$fscores <- fscores[rownames(finalTable)]
Final_Columns <- c("DecorFormula","caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC","RAWAUC","fscores")
finalTable <- finalTable[order(-finalTable$ROCAUC),]
pander::pander(finalTable[,Final_Columns])| DecorFormula | caseMean | caseStd | controlMean | controlStd | controlKSP | ROCAUC | RAWAUC | fscores | |
|---|---|---|---|---|---|---|---|---|---|
| original_firstorder_Skewness | NA | -3.93e-02 | 5.28e-01 | -6.84e-01 | 6.34e-01 | 9.78e-01 | 0.780 | 0.780 | NA |
| original_firstorder_Skewness1 | NA | -3.93e-02 | 5.28e-01 | -6.84e-01 | 6.34e-01 | 9.78e-01 | 0.780 | NA | NA |
| La_wavelet.HLL_glszm_SmallAreaHighGrayLevelEmphasis | - (0.428)wavelet.HLL_gldm_SmallDependenceHighGrayLevelEmphasis - (0.559)wavelet.HLL_glszm_HighGrayLevelZoneEmphasis + wavelet.HLL_glszm_SmallAreaHighGrayLevelEmphasis | -5.51e+01 | 5.85e+01 | 2.27e+01 | 1.23e+02 | 4.20e-02 | 0.762 | 0.517 | -2 |
| La_wavelet.LHL_glszm_GrayLevelNonUniformity | - (3.40e-08)original_firstorder_Energy + wavelet.LHL_glszm_GrayLevelNonUniformity | 9.54e+00 | 7.66e+00 | 2.05e+00 | 6.86e+00 | 5.63e-01 | 0.761 | 0.607 | 0 |
| original_glcm_ClusterShade | NA | 7.42e+02 | 1.02e+04 | -1.06e+04 | 1.65e+04 | 4.41e-02 | 0.755 | 0.755 | NA |
| original_glcm_ClusterShade1 | NA | 7.42e+02 | 1.02e+04 | -1.06e+04 | 1.65e+04 | 4.41e-02 | 0.755 | NA | NA |
| La_wavelet.HLL_firstorder_RobustMeanAbsoluteDeviation | - (0.429)wavelet.HLL_firstorder_InterquartileRange + wavelet.HLL_firstorder_RobustMeanAbsoluteDeviation | -5.45e-02 | 7.68e-01 | 6.93e-01 | 1.20e+00 | 8.69e-02 | 0.746 | 0.511 | -1 |
| La_wavelet.LHL_firstorder_10Percentile | + wavelet.LHL_firstorder_10Percentile + (33.267)wavelet.LHL_glcm_DifferenceEntropy | 8.93e+01 | 5.91e+00 | 8.29e+01 | 8.62e+00 | 1.14e-01 | 0.744 | 0.539 | -1 |
| wavelet.HLL_glcm_ClusterShade | NA | -7.99e+02 | 3.12e+03 | 2.32e+03 | 4.29e+03 | 4.72e-02 | 0.737 | 0.737 | NA |
| wavelet.HLL_glcm_ClusterShade1 | NA | -7.99e+02 | 3.12e+03 | 2.32e+03 | 4.29e+03 | 4.72e-02 | 0.737 | NA | NA |
| wavelet.HLL_firstorder_Skewness | NA | -1.05e-02 | 5.50e-01 | 5.21e-01 | 8.55e-01 | 5.54e-02 | 0.736 | 0.736 | NA |
| wavelet.HLL_firstorder_Skewness1 | NA | -1.05e-02 | 5.50e-01 | 5.21e-01 | 8.55e-01 | 5.54e-02 | 0.736 | NA | NA |
| La_wavelet.HLL_gldm_DependenceNonUniformity | - (5.20e-07)original_firstorder_Energy + wavelet.HLL_gldm_DependenceNonUniformity | 1.88e+02 | 1.34e+02 | 6.86e+01 | 1.35e+02 | 7.20e-01 | 0.734 | 0.591 | 5 |
| original_firstorder_Median | NA | 2.77e+02 | 5.52e+01 | 3.33e+02 | 8.63e+01 | 6.29e-01 | 0.732 | 0.732 | NA |
| La_wavelet.HLL_gldm_HighGrayLevelEmphasis | + wavelet.HLL_gldm_HighGrayLevelEmphasis - (0.996)wavelet.HLL_glszm_HighGrayLevelZoneEmphasis | -2.31e+01 | 3.90e+01 | -6.66e+01 | 6.62e+01 | 3.17e-01 | 0.731 | 0.503 | 0 |
| original_glcm_MaximumProbability | NA | 6.19e-03 | 2.32e-03 | 1.02e-02 | 6.26e-03 | 7.10e-02 | 0.722 | 0.722 | NA |
| original_gldm_LargeDependenceHighGrayLevelEmphasis | NA | 1.36e+04 | 9.87e+03 | 3.19e+04 | 3.44e+04 | 2.54e-03 | 0.711 | 0.711 | NA |
| original_glcm_JointEnergy | NA | 1.72e-03 | 7.60e-04 | 2.89e-03 | 2.23e-03 | 1.21e-02 | 0.710 | 0.710 | NA |
| original_firstorder_Mean | NA | 2.75e+02 | 5.33e+01 | 3.20e+02 | 7.86e+01 | 3.40e-01 | 0.702 | 0.702 | NA |
| original_glszm_LargeAreaHighGrayLevelEmphasis | NA | 2.34e+04 | 4.63e+04 | 1.77e+05 | 7.31e+05 | 1.50e-08 | 0.700 | 0.700 | NA |
1.10 Comparing IDeA vs PCA vs EFA
1.10.1 PCA
featuresnames <- colnames(dataframe)[colnames(dataframe) != outcome]
pc <- prcomp(dataframe[,iscontinous],center = TRUE,scale. = TRUE) #principal components
predPCA <- predict(pc,dataframe[,iscontinous])
PCAdataframe <- as.data.frame(cbind(predPCA,dataframe[,!iscontinous]))
colnames(PCAdataframe) <- c(colnames(predPCA),colnames(dataframe)[!iscontinous])
#plot(PCAdataframe[,colnames(PCAdataframe)!=outcome],col=dataframe[,outcome],cex=0.65,cex.lab=0.5,cex.axis=0.75,cex.sub=0.5,cex.main=0.75)
#pander::pander(pc$rotation)
PCACor <- cor(PCAdataframe[,colnames(PCAdataframe) != outcome])
gplots::heatmap.2(abs(PCACor),
trace = "none",
# scale = "row",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "PCA Correlation",
cexRow = 0.5,
cexCol = 0.5,
srtCol=45,
srtRow= -45,
key.title=NA,
key.xlab="Pearson Correlation",
xlab="Feature", ylab="Feature")
1.10.2 EFA
EFAdataframe <- dataframeScaled
if (length(iscontinous) < 2000)
{
topred <- min(length(iscontinous),nrow(dataframeScaled),ncol(predPCA)/2)
if (topred < 2) topred <- 2
uls <- fa(dataframeScaled[,iscontinous],nfactors=topred,rotate="varimax",warnings=FALSE) # EFA analysis
predEFA <- predict(uls,dataframeScaled[,iscontinous])
EFAdataframe <- as.data.frame(cbind(predEFA,dataframeScaled[,!iscontinous]))
colnames(EFAdataframe) <- c(colnames(predEFA),colnames(dataframeScaled)[!iscontinous])
EFACor <- cor(EFAdataframe[,colnames(EFAdataframe) != outcome])
gplots::heatmap.2(abs(EFACor),
trace = "none",
# scale = "row",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "EFA Correlation",
cexRow = 0.5,
cexCol = 0.5,
srtCol=45,
srtRow= -45,
key.title=NA,
key.xlab="Pearson Correlation",
xlab="Feature", ylab="Feature")
}
1.11 Effect on CAR modeling
par(op)
par(xpd = TRUE)
dataframe[,outcome] <- factor(dataframe[,outcome])
rawmodel <- rpart(paste(outcome,"~."),dataframe,control=rpart.control(maxdepth=3))
pr <- predict(rawmodel,dataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
plot(rawmodel,main="Raw",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
text(rawmodel, use.n = TRUE,cex=0.75)
ptab <- epiR::epi.tests(table(pr==0,dataframe[,outcome]==0))
}
pander::pander(table(dataframe[,outcome],pr))| 0 | 1 | |
|---|---|---|
| 0 | 46 | 8 |
| 1 | 9 | 87 |
pander::pander(ptab$detail[c(5,3,4,6),])| statistic | est | lower | upper | |
|---|---|---|---|---|
| 5 | diag.ac | 0.887 | 0.825 | 0.933 |
| 3 | se | 0.906 | 0.829 | 0.956 |
| 4 | sp | 0.852 | 0.729 | 0.934 |
| 6 | diag.or | 55.583 | 20.099 | 153.711 |
par(op)
par(xpd = TRUE)
DEdataframe[,outcome] <- factor(DEdataframe[,outcome])
IDeAmodel <- rpart(paste(outcome,"~."),DEdataframe,control=rpart.control(maxdepth=3))
pr <- predict(IDeAmodel,DEdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
plot(IDeAmodel,main="IDeA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
text(IDeAmodel, use.n = TRUE,cex=0.75)
ptab <- epiR::epi.tests(table(pr==0,DEdataframe[,outcome]==0))
}
pander::pander(table(DEdataframe[,outcome],pr))| 0 | 1 | |
|---|---|---|
| 0 | 44 | 10 |
| 1 | 8 | 88 |
pander::pander(ptab$detail[c(5,3,4,6),])| statistic | est | lower | upper | |
|---|---|---|---|---|
| 5 | diag.ac | 0.880 | 0.817 | 0.927 |
| 3 | se | 0.917 | 0.842 | 0.963 |
| 4 | sp | 0.815 | 0.686 | 0.907 |
| 6 | diag.or | 48.400 | 17.847 | 131.255 |
par(op)
par(xpd = TRUE)
PCAdataframe[,outcome] <- factor(PCAdataframe[,outcome])
PCAmodel <- rpart(paste(outcome,"~."),PCAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(PCAmodel,PCAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
plot(PCAmodel,main="PCA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
text(PCAmodel, use.n = TRUE,cex=0.75)
ptab <- epiR::epi.tests(table(pr==0,PCAdataframe[,outcome]==0))
}
pander::pander(table(PCAdataframe[,outcome],pr))| 0 | 1 | |
|---|---|---|
| 0 | 38 | 16 |
| 1 | 14 | 82 |
pander::pander(ptab$detail[c(5,3,4,6),])| statistic | est | lower | upper | |
|---|---|---|---|---|
| 5 | diag.ac | 0.800 | 0.727 | 0.861 |
| 3 | se | 0.854 | 0.767 | 0.918 |
| 4 | sp | 0.704 | 0.564 | 0.820 |
| 6 | diag.or | 13.911 | 6.164 | 31.392 |
par(op)1.11.1 EFA
EFAdataframe[,outcome] <- factor(EFAdataframe[,outcome])
EFAmodel <- rpart(paste(outcome,"~."),EFAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(EFAmodel,EFAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
plot(EFAmodel,main="EFA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
text(EFAmodel, use.n = TRUE,cex=0.75)
ptab <- epiR::epi.tests(table(pr==0,EFAdataframe[,outcome]==0))
}
pander::pander(table(EFAdataframe[,outcome],pr))| 0 | 1 | |
|---|---|---|
| 0 | 42 | 12 |
| 1 | 7 | 89 |
pander::pander(ptab$detail[c(5,3,4,6),])| statistic | est | lower | upper | |
|---|---|---|---|---|
| 5 | diag.ac | 0.873 | 0.809 | 0.922 |
| 3 | se | 0.927 | 0.856 | 0.970 |
| 4 | sp | 0.778 | 0.644 | 0.880 |
| 6 | diag.or | 44.500 | 16.342 | 121.177 |
par(op)